What is the radius (in cm) of the imaginary concentric sphere that divides the electrostatic field of a metal sphere of a radius 20 c m & a charge of 8 μC in two regions of identical energy?

Step-by-step solution

The energy between shell 1 & 2 = e n e r g y behind shell 2. energy between shall 1 & 2 = ∫ r = a r = b 1 2 ε 0 K Q r 2 2 × 4 π r 2 d r = ε 0 K 2 Q 2 2 × 4 π - 1 r a b = ε 0 K 2 Q 2 2 1 a - 1 b Energy beyond shell 2 = ∫ r = b r = ∞ 1 2 ε 0 K Q r 2 2 × 4 π r 2 d r = 1 2 ∈ 0 K 2 Q 2 × 4 π 1 b ∴ 1 2 ε 0 K 2 Q 2 × 4 π 1 a - 1 b = 1 2 ε 0 K 2 Q 2 × 4 π 1 b 1 a = 2 b b = 2a a = 20 cm b = 40 cm